William W. answered • 10/17/23
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A = πr2
The upper boundary of area is 926 in2 and the lower boundary is 924 in2, right?
So calculate the radius at 926 and then again at 924. That gives you the range of acceptable values of the radius. Note: You must be greater than the smaller value and less than the upper value because the are must be LESS then 1 in2 off.
William W.
Sure. Let's just say the area of the disk was 100 square inches and, in order to keep people happy, they want the area to be within 2 square inches of that. So the lower limit of the area would be 98 square inches and the upper limit is 102 square inches. If the final area of the disk was 98 sq in then, using the Area equation A = (pi)(r^2) we would get: 98 = (pi)(r^2) or r = sqrt(98/pi) = 5.585191926 inches (A radius of 5.585191926 inches gives an area of 98 sq in) The upper limit was 102 sq in so 102 = (pi)(r^2) yielding: 102 = (pi)(r^2) or r = sqrt(102/pi) = 5.698035485 inches (A radius of 5.698035485 inches gives an area of 102 sq in) The "perfect" area of 100 sq inches would result in a radius: 100 = (pi)(r^2) or r = sqrt(100/pi) = 5.641895835 inches (A radius of 5.641895835 inches gives an area of 100 sq in) The radius of the lower limit was off by (5.641895835 - 5.585191926) or 0.056703909 inches. The radius of the upper limit was off by (5.698035485 - 5.641895835) or 0.05613965 inches Since the question asks for a single answer, pick the smaller of the two to ensure you are within the requirements. The radius must be off by less than 0.05613965 inches
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10/19/23
Kalab T.
can you elaborate with a example?10/18/23